Citation and License

Boundary Value Problems 2012, 2012:5
doi:10.1186/1687-2770-2012-5

Published: 17 January 2012

Abstract

We consider the static deflection of an infinite beam resting on a nonlinear and non-uniform
elastic foundation. The governing equation is a fourth-order nonlinear ordinary differential
equation. Using the Green's function for the well-analyzed linear version of the equation,
we formulate a new integral equation which is equivalent to the original nonlinear
equation. We find a function space on which the corresponding nonlinear integral operator
is a contraction, and prove the existence and the uniqueness of the deflection in
this function space by using Banach fixed point theorem.